This paper describes our experience with global lens optimization using algorithms that can modify an existing lens
construction in an optimal way or create an entirely new construction. The binary-search method assembles lens
elements according to the bits in a binary number, ensuring that all combinations of power are tested, while the saddlepoint
method can either add elements to a starting lens or start from scratch. The latter algorithm also naturally leads to a
method of removing an element in an optimum way, which can sometimes simplify a lens with no loss of quality.